The function h = -t2 + 95 models the path of a ball thrown by a boy where h represents height, in feet, and t represents the time, in seconds, that the ball is in the air. assuming the boy lives at sea level where h = 0 ft, which is a likely place the boy could have been standing when he threw this ball?

A building where the boy is on the 12 floor

Explanation:

The equation of the height or position takes into account the initial conditions.

So the general equation is

x(t) = at+c

When you solve with the initial conditions t=0 you will find the position at the begining, so this is c the constant.

in our initial equation we have 95 as the constant. and this is a equation to find height so the initial height is 95feets.

Now a common building has a distance of 7.5 feet between every floor.

You divide 95 by 7.5 and you will find 12.6

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .